Vulnerability of electronic systems and particularly computing systems to malicious attacks through the insertion of software viruses or hardware Trojans is of growing concern to society. This work is focused on understanding, detecting, and mitigating a potentially devastating type of hardware Trojans that an adversary or hardware hacker can insert in the analog component of many of the integrated circuits that will be fabricated in the future. The class of analog hardware Trojans that will be studied are those that can be embedded as undesired solutions of the nonlinear differential equations that mathematically characterize the performance of an analog circuit that is typical of a design that would be obtained from a highly qualified and trusted design engineer. This class of hardware Trojans is particularly problematic because their presence will typically not be observed through computer simulations during the normal design or verification processes. Although the payloads these hardware Trojans can carry can be devastating, existing methods for Trojan detection or prevention are inherently incapable of detecting or preventing this type of Trojans. An improved understanding of the vulnerabilities to these Trojans will be developed along with methods for detecting and mitigating the vulnerabilities. By reducing vulnerability to these hardware Trojans, a more secure cyber infrastructure can be developed. This should improve security of transportation, health care, financial, and military systems. Research results including prototype circuits will be accessible on https://iastate.box.com/s/nazel2i7n5ygk6jy8yawvsnsynmk4qh7. This URL will remain active for 3 years after public release and project completion.